General asymptotic confidence bands based on kernel-type function estimators. (English) Zbl 1125.62314
Summary: We establish uniform and non-uniform asymptotic simultaneous confidence bands for functionals of the distribution based on kernel-type estimators, which include the Nadaraya-Watson kernel estimators of regression functions and the Akaike-Parzen-Rosenblatt kernel density estimators. Our theorems, based upon functional limit laws derived by modern empirical process theory, allow data-driven local bandwidths for these statistics.
MSC:
62G07 | Density estimation |
62G15 | Nonparametric tolerance and confidence regions |
62G08 | Nonparametric regression and quantile regression |
60F15 | Strong limit theorems |